//Given the root of a complete binary tree, return the number of the nodes in th
//e tree. 
//
// According to Wikipedia, every level, except possibly the last, is completely 
//filled in a complete binary tree, and all nodes in the last level are as far lef
//t as possible. It can have between 1 and 2h nodes inclusive at the last level h.
// 
//
// Design an algorithm that runs in less than O(n) time complexity. 
//
// 
// Example 1: 
//
// 
//Input: root = [1,2,3,4,5,6]
//Output: 6
// 
//
// Example 2: 
//
// 
//Input: root = []
//Output: 0
// 
//
// Example 3: 
//
// 
//Input: root = [1]
//Output: 1
// 
//
// 
// Constraints: 
//
// 
// The number of nodes in the tree is in the range [0, 5 * 104]. 
// 0 <= Node.val <= 5 * 104 
// The tree is guaranteed to be complete. 
// 
// Related Topics 树 深度优先搜索 二分查找 二叉树 
// 👍 535 👎 0

package leetcode.editor.cn;
 class P222CountCompleteTreeNodes {
    public static void main(String[] args) {
        Solution solution = new P222CountCompleteTreeNodes().new Solution();

    }
    //leetcode submit region begin(Prohibit modification and deletion)
/**
 * Definition for a binary tree node.
 * public class TreeNode {
 *     int val;
 *     TreeNode left;
 *     TreeNode right;
 *     TreeNode() {}
 *     TreeNode(int val) { this.val = val; }
 *     TreeNode(int val, TreeNode left, TreeNode right) {
 *         this.val = val;
 *         this.left = left;
 *         this.right = right;
 *     }
 * }
 */
class Solution {
    public int countNodes(TreeNode root) {
        if (root == null) {
            return 0;
        }
        int left = countNodes(root.left);
        int right = countNodes(root.right);
        return left + right+1;
    }
    public int countNodesB(TreeNode root) {
        if (root == null) {
            return 0;
        }
        int level = 0;
        TreeNode node = root;
        while (node.left != null) {
            level++;
            node = node.left;
        }
        int low = 1 << level, high = (1 << (level + 1)) - 1;
        while (low < high) {
            int mid = (high - low + 1) / 2 + low;
            if (exists(root, level, mid)) {
                low = mid;
            } else {
                high = mid - 1;
            }
        }
        return low;
    }

    public boolean exists(TreeNode root, int level, int k) {
        int bits = 1 << (level - 1);
        TreeNode node = root;
        while (node != null && bits > 0) {
            if ((bits & k) == 0) {
                node = node.left;
            } else {
                node = node.right;
            }
            bits >>= 1;
        }
        return node != null;
    }

}
//leetcode submit region end(Prohibit modification and deletion)

}